Relational interpretation of the wave function and a possible way around Bell's theorem

The famous ``spooky action at a distance'' in the EPR-szenario is shown to be a local interaction, once entanglement is interpreted as a kind of ``nearest neighbor'' relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the ``nearest neighbor'' relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, ``position'' becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the ``weird'' aspects, like the particle-wave duality, the non-locality of entanglement, or the ``mystery'' of the double-slit experiment, disappear. Furthermore, this picture cirumvents the restrictions set by Bell's inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics.Comment: Accepted for publication in "International Journal of Theoretical Physics

Bregman Voronoi Diagrams: Properties, Algorithms and Applications

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow to define information-theoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently. We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connexion with Bregman Voronoi diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation. Finally, we give some applications of Bregman Voronoi diagrams which are of interest in the context of computational geometry and machine learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures

Embodied cognitive ecosophy: the relationship of mind, body, meaning and ecology

The concept of embodied cognition has had a major impact in a number of disciplines. The extent of its consequences on general knowledge and epistemology are still being explored. Embodied cognition in human geography has its own traditions and discourses but these have become somewhat isolated in the discipline itself. This paper argues that findings in other disciplines are of value in reconceptualising embodied cognition in human geography and this is explored by reconsidering the concept of ecosophy. Criticisms of ecosophy as a theory are considered and recent work in embodied cognition is applied to consider how such criticisms might be addressed. An updated conceptualisation is proposed, the embodied cognitive ecosophy, and three characteristics arising from this criticism and synthesis are presented with a view to inform future discussions of ecosophy and emotional geography

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Mild orotic aciduria in UMPS heterozygotes: a metabolic finding without clinical consequences

BACKGROUND: Elevated urinary excretion of orotic acid is associated with treatable disorders of the urea cycle and pyrimidine metabolism. Establishing the correct and timely diagnosis in a patient with orotic aciduria is key to effective treatment. Uridine monophosphate synthase is involved in de novo pyrimidine synthesis. Uridine monophosphate synthase deficiency (or hereditary orotic aciduria), due to biallelic mutations in UMPS, is a rare condition presenting with megaloblastic anemia in the first months of life. If not treated with the pyrimidine precursor uridine, neutropenia, failure to thrive, growth retardation, developmental delay, and intellectual disability may ensue. METHODS AND RESULTS: We identified mild and isolated orotic aciduria in 11 unrelated individuals with diverse clinical signs and symptoms, the most common denominator being intellectual disability/developmental delay. Of note, none had blood count abnormalities, relevant hyperammonemia or altered plasma amino acid profile. All individuals were found to have heterozygous alterations in UMPS. Four of these variants were predicted to be null alleles with complete loss of function. The remaining variants were missense changes and predicted to be damaging to the normal encoded protein. Interestingly, family screening revealed heterozygous UMPS variants in combination with mild orotic aciduria in 19 clinically asymptomatic family members. CONCLUSIONS: We therefore conclude that heterozygous UMPS-mutations can lead to mild and isolated orotic aciduria without clinical consequence. Partial UMPS-deficiency should be included in the differential diagnosis of mild orotic aciduria. The discovery of heterozygotes manifesting clinical symptoms such as hypotonia and developmental delay are likely due to ascertainment bias

Monsters, Laws of Nature, and Teleology in Late Scholastic Textbooks

In the period of emergence of early modern science, ‘monsters’ or individuals with physical congenital anomalies were considered as rare events which required special explanations entailing assumptions about the laws of nature. This concern with monsters was shared by representatives of the new science and Late Scholastic authors of university textbooks. This paper will reconstruct the main theses of the treatment of monsters in Late Scholastic textbooks, by focusing on the question as to how their accounts conceived nature’s regularity and teleology. It shows that they developed a naturalistic teratology in which, in contrast to the naturalistic explanations usually offered by the new science, finality was at central stage. This general point does not impede our noticing that some authors were closer to the views emerging in the Scientific Revolution insofar as they conceived nature as relatively autonomous from God and gave a relevant place to efficient secondary causation. In this connection, this paper suggests that the concept of the laws of nature developed by the new science –as exception-less regularities—transferred to nature’s regularity the ‘strong’ character that Late Scholasticism attributed to finality and that the decline of the Late Scholastic view of finality played as an important concomitant factor permitting the transformation of the concept of laws of nature